mirror of
https://github.com/3b1b/manim.git
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899 lines
23 KiB
Python
899 lines
23 KiB
Python
#!/usr/bin/env python
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# -*- coding: utf-8 -*-
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from manimlib.imports import *
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class SimpleVelocityGraph(GraphScene):
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CONFIG = {
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# "frame_rate" : 4000,
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# "domino_thickness" : 7.5438,
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# "domino_spacing" : 8.701314282,
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"data_files" : [
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"data07.txt",
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"data13.txt",
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# "data11.txt",
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],
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"colors" : [WHITE, BLUE, YELLOW, GREEN, MAROON_B],
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"x_axis_label" : "$t$",
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"y_axis_label" : "$v$",
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"x_min" : 0,
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"x_max" : 1.8,
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"x_tick_frequency" : 0.1,
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"x_labeled_nums" : np.arange(0, 1.8, 0.2),
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"y_tick_frequency" : 100,
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"y_min" : 0,
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"y_max" : 1000,
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"y_labeled_nums" : list(range(0, 1000, 200)),
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"x_axis_width" : 12,
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"graph_origin" : 2.5*DOWN + 5*LEFT,
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"trailing_average_length" : 20,
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"include_domino_thickness" : False,
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}
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def construct(self):
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self.setup_axes()
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# self.save_all_images()
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for data_file, color in zip(self.data_files, self.colors):
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self.init_data(data_file)
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self.draw_dots(color)
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self.add_label_to_last_dot(
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"%s %s %.2f"%(
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data_file[4:6],
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"hard" if self.friction == "low" else "felt",
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self.domino_spacing,
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),
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color
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)
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self.draw_lines(color)
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def save_all_images(self):
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indices = list(range(1, 20))
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for i1, i2 in it.combinations(indices, 2):
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to_remove = VGroup()
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for index in i1, i2:
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index_str = ("%.2f"%float(0.01*index))[-2:]
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data_file = "data%s.txt"%index_str
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self.init_data(data_file)
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color = WHITE if self.friction == "low" else BLUE
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self.draw_dots(color)
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self.add_label_to_last_dot(
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"%s %s %.2f"%(
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data_file[4:6],
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"hard" if self.friction == "low" else "felt",
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self.domino_spacing,
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),
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color
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)
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self.draw_lines(color)
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to_remove.add(self.dots, self.lines, self.label)
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self.save_image("dominos_%d_vs_%d"%(i1, i2))
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self.remove(to_remove)
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def init_data(self, data_file):
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file_name = os.path.join(
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os.path.dirname(os.path.realpath(__file__)),
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"dominos",
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data_file
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)
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file = open(file_name, "r")
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frames, notes = [], []
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for line in file:
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line = line.replace(" ", ",")
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line = line.replace("\n", "")
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entries = [s for s in line.split(",") if s is not ""]
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if len(entries) == 0:
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continue
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if entries[0] == "framerate":
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frame_rate = float(entries[1])
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elif entries[0] == "domino spacing":
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domino_spacing = float(entries[1])
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elif entries[0] == "domino thickness":
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domino_thickness = float(entries[1])
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elif entries[0] == "friction":
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self.friction = entries[1]
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else:
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try:
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frames.append(int(entries[0]))
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except:
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continue #How to treat?
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# frames.append(frames[-1] + (frames[-1] - frames[-2]))
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if len(entries) > 1:
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notes.append(entries[1])
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else:
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notes.append("")
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frames = np.array(frames)
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self.times = (frames - frames[0])/float(frame_rate)
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delta_times = self.times[1:] - self.times[:-1]
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if self.include_domino_thickness:
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distance = domino_spacing+domino_thickness
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else:
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distance = domino_spacing
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self.velocities = distance/delta_times
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self.notes = notes
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n = self.trailing_average_length
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self.velocities = np.array([
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np.mean(self.velocities[max(0, i-n):i])
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for i in range(len(self.velocities))
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])
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self.domino_spacing = domino_spacing
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self.domino_thickness = domino_thickness
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def draw_dots(self, color = WHITE):
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dots = VGroup()
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for time, v, note in zip(self.times, self.velocities, self.notes):
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dot = Dot(color = color)
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dot.scale(0.5)
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dot.move_to(self.coords_to_point(time, v))
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self.add(dot)
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dots.add(dot)
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if note == "twist":
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dot.set_color(RED)
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self.dots = dots
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def add_label_to_last_dot(self, label, color = WHITE):
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dot = self.dots[-1]
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label = TextMobject(label)
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label.scale(0.75)
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label.next_to(dot, UP, buff = MED_SMALL_BUFF)
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label.set_color(color)
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label.shift_onto_screen()
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self.label = label
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self.add(label)
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def draw_lines(self, color = WHITE, stroke_width = 2):
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lines = VGroup()
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for d1, d2 in zip(self.dots, self.dots[1:]):
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line = Line(d1.get_center(), d2.get_center())
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lines.add(line)
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lines.set_stroke(color, stroke_width)
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self.add(lines, self.dots)
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self.lines = lines
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ALL_VELOCITIES = {
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10 : [
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0.350308642,
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0.3861880046,
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0.8665243271,
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0.9738947062,
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0.8087560386,
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1.067001275,
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0.9059117965,
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1.113855622,
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0.9088626493,
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1.504155436,
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1.347926731,
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1.274067732,
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1.242854491,
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1.118319973,
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1.177303094,
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1.202676006,
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0.9965029762,
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1.558775605,
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1.472405453,
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1.357765612,
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1.200089606,
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1.285810292,
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1.138860544,
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1.322373618,
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1.51230804,
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1.148233882,
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1.276983219,
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1.150601375,
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1.492090018,
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1.210502531,
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1.221097739,
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1.141189502,
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1.364405053,
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1.608189241,
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1.223775585,
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1.174824561,
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1.069045338,
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1.468530702,
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1.733048654,
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1.328670635,
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1.118319973,
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1.143528005,
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1.010945048,
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1.430876068,
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1.395104167,
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1.018324209,
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1.405646516,
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1.120565596,
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1.24562872,
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1.65590999,
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1.276983219,
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1.282854406,
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1.338229416,
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1.240092593,
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0.9982856291,
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1.811823593,
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1.328670635,
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1.167451185,
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1.27991208,
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1.221097739,
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1.022054335,
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1.160169785,
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1.805960086,
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0.9965029762,
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1.449458874,
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1.603568008,
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1.234605457,
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1.210502531,
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1.192396724,
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1.020185862,
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1.496090259,
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1.322373618,
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1.291763117,
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1.210502531,
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0.9807410662,
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1.341446314,
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1.391625104,
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1.480216622,
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1.148233882,
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1.125084005,
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1.670783433,
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1.118319973,
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1.174824561,
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1.395104167,
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1.167451185,
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1.182291667,
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1.696175279,
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1.306889149,
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1.430876068,
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1.048950501,
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1.823665577,
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1.24562872,
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],
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13 : [
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0.2480920273,
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0.3532654568,
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0.549163523,
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0.5979017857,
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0.6643353175,
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0.8495940117,
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1.037573598,
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0.897413562,
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1.410977665,
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0.9180833562,
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1.303328143,
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0.9324004456,
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2.026785714,
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0.9721980256,
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1.339835934,
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1.002770291,
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2.3797086,
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1.235972684,
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1.508900406,
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1.239174685,
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1.374486864,
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1.181040564,
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1.144309638,
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1.195803571,
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1.265400605,
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1.223328462,
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1.678320802,
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1.198800573,
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0.7958759211,
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1.573425752,
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1.046655205,
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2.009753902,
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1.42782516,
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1.289276088,
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1.347384306,
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1.299786491,
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1.06530385,
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1.339835934,
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1.242393321,
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1.053571429,
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1.317689886,
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1.626943635,
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1.112375415,
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1.362739113,
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0.9110884354,
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1.578618576,
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1.853959025,
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1.504155436,
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1.158163265,
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1.262061817,
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1.060579664,
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1.122820255,
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1.594404762,
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1.27552381,
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1.382431874,
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1.109794498,
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1.303328143,
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1.160974341,
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1.296264034,
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1.092058056,
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1.077300515,
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1.462756662,
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1.317689886,
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1.390469269,
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1.099589491,
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1.649384236,
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1.467243646,
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1.402702137,
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1.092058056,
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1.201812635,
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1.258740602,
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1.321329913,
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1.272131459,
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1.175236925,
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1.181040564,
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1.296264034,
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1.24562872,
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1.358867695,
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1.332371667,
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1.296264034,
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1.217102872,
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1.169490045,
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1.114968365,
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1.528183478,
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1.374486864,
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1.223328462,
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1.324990107,
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1.268757105,
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1.169490045,
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1.578618576,
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],
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14 : [
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0.4905860806,
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0.6236263736,
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0.71391258,
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0.8436004031,
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1.048950501,
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0.9585599771,
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1.138860544,
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1.210940325,
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1.27552381,
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1.282363079,
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1.166637631,
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1.242393321,
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1.163799096,
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1.166637631,
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1.42357568,
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1.382431874,
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1.278934301,
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1.390469269,
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1.181040564,
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1.107225529,
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1.08462909,
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1.160974341,
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1.374486864,
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1.382431874,
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1.355018211,
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1.25543682,
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1.192821518,
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0.9360497624,
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1.449458874,
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1.370548506,
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1.485470275,
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1.471758242,
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1.149811126,
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1.217102872,
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1.152581756,
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1.402702137,
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1.155365769,
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1.141578588,
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1.248881015,
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1.074879615,
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1.453864525,
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1.303328143,
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1.248881015,
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1.169490045,
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1.214013778,
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1.220207726,
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1.310469667,
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1.42357568,
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1.163799096,
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1.220207726,
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1.141578588,
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1.207882395,
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1.104668426,
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1.328670635,
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1.25543682,
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1.239174685,
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1.169490045,
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1.149811126,
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1.000672445,
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1.144309638,
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1.232787187,
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1.268757105,
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1.306889149,
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1.538011024,
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1.355018211,
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1.347384306,
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1.223328462,
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1.149811126,
|
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1.158163265,
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1.24562872,
|
|
1.485470275,
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|
1.339835934,
|
|
1.314069859,
|
|
1.235972684,
|
|
1.265400605,
|
|
1.181040564,
|
|
1.638087084,
|
|
1.568266979,
|
|
1.299786491,
|
|
1.278934301,
|
|
1.336093376,
|
|
1.089570452,
|
|
1.004876951,
|
|
1.089570452,
|
|
1.282363079,
|
|
1.449458874,
|
|
1.370548506,
|
|
1.265400605,
|
|
1.143215651,
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|
],
|
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15 : [
|
|
1.087094156,
|
|
1.223328462,
|
|
1.563141923,
|
|
1.394523115,
|
|
1.268757105,
|
|
1.513675407,
|
|
1.436400686,
|
|
1.094557045,
|
|
0.9761661808,
|
|
1.072469571,
|
|
1.178131597,
|
|
1.366632653,
|
|
1.258740602,
|
|
1.25543682,
|
|
1.285810292,
|
|
1.235972684,
|
|
1.347384306,
|
|
1.239174685,
|
|
1.195803571,
|
|
1.186901808,
|
|
1.141578588,
|
|
1.152581756,
|
|
1.136155412,
|
|
1.102123107,
|
|
1.242393321,
|
|
1.347384306,
|
|
1.278934301,
|
|
1.366632653,
|
|
1.351190476,
|
|
0.9882674144,
|
|
1.1898543,
|
|
1.351190476,
|
|
1.169490045,
|
|
1.292760618,
|
|
1.638087084,
|
|
1.436400686,
|
|
1.328670635,
|
|
1.242393321,
|
|
1.355018211,
|
|
1.303328143,
|
|
1.186901808,
|
|
1.112375415,
|
|
1.432100086,
|
|
1.1898543,
|
|
1.324990107,
|
|
1.074879615,
|
|
1.214013778,
|
|
1.20483987,
|
|
1.158163265,
|
|
1.112375415,
|
|
1.220207726,
|
|
1.402702137,
|
|
1.268757105,
|
|
1.282363079,
|
|
1.289276088,
|
|
1.292760618,
|
|
1.183963932,
|
|
1.252150337,
|
|
1.42782516,
|
|
1.292760618,
|
|
1.026440834,
|
|
1.268757105,
|
|
1.268757105,
|
|
1.285810292,
|
|
1.347384306,
|
|
1.272131459,
|
|
1.220207726,
|
|
1.296264034,
|
|
1.25543682,
|
|
1.494754464,
|
|
1.347384306,
|
|
1.214013778,
|
|
1.169490045,
|
|
1.147053786,
|
|
1.082175178,
|
|
1.109794498,
|
|
1.382431874,
|
|
1.24562872,
|
|
1.201812635,
|
|
1.328670635,
|
|
1.122820255,
|
|
1.220207726,
|
|
1.192821518,
|
|
1.563141923,
|
|
1.41935142,
|
|
1.336093376,
|
|
1.406827731,
|
|
1.258740602,
|
|
1.186901808,
|
|
1.232787187,
|
|
1.107225529,
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],
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}
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# Felt: 8,9,10,11,12,13
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# Hardwood 1-7, 14,15
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class ContrastTwoGraphs(SimpleVelocityGraph):
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CONFIG = {
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"velocities1_index" : 13,
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"velocities2_index" : 14,
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"x_min" : -1,
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"x_max" : 10,
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"y_min" : -0.25,
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"y_max" : 2,
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"x_axis_label" : "",
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"y_axis_label" : "",
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"x_labeled_nums" : [],
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"y_labeled_nums" : [],
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"y_tick_frequency" : 0.25,
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"x_tick_frequency" : 12,
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"moving_average_n" : 20,
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}
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def construct(self):
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self.setup_axes()
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velocities1 = ALL_VELOCITIES[self.velocities1_index]
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velocities2 = ALL_VELOCITIES[self.velocities2_index]
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self.n_data_points = len(velocities1)
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graph1 = self.get_velocity_graph(velocities1)
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graph2 = self.get_velocity_graph(velocities2)
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smoothed_graph1 = self.get_smoothed_velocity_graph(velocities1)
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smoothed_graph2 = self.get_smoothed_velocity_graph(velocities2)
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for graph in graph1, smoothed_graph1:
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self.color_graph(graph)
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for graph in graph2, smoothed_graph2:
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self.color_graph(graph, BLUE, RED)
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for graph in graph1, graph2, smoothed_graph1, smoothed_graph2:
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graph.axes = self.axes.deepcopy()
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graph.add_to_back(graph.axes)
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lower_left = self.axes.get_corner(DOWN+LEFT)
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self.remove(self.axes)
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felt = TextMobject("Felt")
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hardwood = TextMobject("Hardwood")
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hardwood.set_color(RED)
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words = VGroup(felt, hardwood)
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self.force_skipping()
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#Show jaggediness
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graph1.scale(0.5).to_edge(UP)
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graph2.scale(0.5).to_edge(DOWN)
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felt.next_to(graph1, LEFT, buff = 0.75)
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hardwood.next_to(graph2, LEFT, buff = 0.75)
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self.play(
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ShowCreation(graph1, run_time = 3, rate_func=linear),
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Write(felt)
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)
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self.play(
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ShowCreation(graph2, run_time = 4, rate_func=linear),
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Write(hardwood)
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)
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self.wait()
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for g, sg in (graph1, smoothed_graph1), (graph2, smoothed_graph2):
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sg_copy = sg.deepcopy()
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sg_copy.scale(0.5)
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sg_copy.shift(g.get_center())
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mover = VGroup(*it.chain(*list(zip(g.dots, g.lines))))
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target = VGroup(*it.chain(*list(zip(sg_copy.dots, sg_copy.lines))))
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for m, t in zip(mover, target):
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m.target = t
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self.play(LaggedStartMap(
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MoveToTarget, mover,
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rate_func = lambda t : 0.3*wiggle(t),
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run_time = 3,
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lag_ratio = 0.2,
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))
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twists = TextMobject("Twists?")
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variable_distances = TextMobject("Variable distances")
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for word in twists, variable_distances:
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word.to_corner(UP+RIGHT)
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self.play(Write(twists))
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self.wait()
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self.play(ReplacementTransform(twists, variable_distances))
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self.wait(3)
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self.play(FadeOut(variable_distances))
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self.revert_to_original_skipping_status()
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self.play(
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graph1.scale, 2,
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graph1.move_to, lower_left, DOWN+LEFT,
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graph2.scale, 2,
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graph2.move_to, lower_left, DOWN+LEFT,
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FadeOut(words)
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)
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self.wait()
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return
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#Show moving averages
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self.play(FadeOut(graph2))
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dots = graph1.dots
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dot1, dot2 = dots[21], dots[41]
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rect = Rectangle(
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width = dot2.get_center()[0] - dot1.get_center()[0],
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height = FRAME_Y_RADIUS - self.x_axis.get_center()[1],
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stroke_width = 0,
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fill_color = YELLOW,
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fill_opacity = 0.5
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)
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rect.move_to(dot2.get_center(), RIGHT)
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rect.to_edge(UP, buff = 0)
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pre_rect = rect.copy()
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pre_rect.stretch_to_fit_width(0)
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pre_rect.move_to(rect, RIGHT)
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arrow = Vector(DOWN)
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arrow.next_to(dot2, UP, SMALL_BUFF)
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self.play(GrowArrow(arrow))
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self.play(
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dot2.shift, MED_SMALL_BUFF*UP,
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dot2.set_color, PINK,
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rate_func = wiggle
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)
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self.wait()
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self.play(
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FadeOut(arrow),
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ReplacementTransform(pre_rect, rect),
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)
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self.wait()
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self.play(
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Transform(graph1, smoothed_graph1, run_time = 2),
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Animation(rect)
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)
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self.play(FadeOut(rect))
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self.wait()
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self.play(FadeIn(graph2))
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self.play(Transform(graph2, smoothed_graph2))
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felt.next_to(dot2, UP, MED_LARGE_BUFF)
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hardwood.next_to(felt, DOWN, LARGE_BUFF)
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self.play(
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LaggedStartMap(FadeIn, felt),
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LaggedStartMap(FadeIn, hardwood),
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run_time = 1
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)
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self.wait()
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#Compare regions
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dot_group1 = VGroup(
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*graph1.dots[35:75] + graph2.dots[35:75]
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)
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dot_group2 = VGroup(
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*graph1.dots[75:] + graph2.dots[75:]
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)
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dot_group3 = VGroup(
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*graph1.dots[35:] + graph2.dots[35:]
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)
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rect1 = SurroundingRectangle(dot_group1)
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rect2 = SurroundingRectangle(dot_group2)
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rect3 = SurroundingRectangle(dot_group3)
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self.play(ShowCreation(rect1))
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for x in range(2):
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self.play(LaggedStartMap(
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ApplyMethod, dot_group1,
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lambda m : (m.scale_in_place, 0.5),
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rate_func = wiggle,
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lag_ratio = 0.05,
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run_time = 3,
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))
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self.wait()
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self.play(ReplacementTransform(rect1, rect2))
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for x in range(2):
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self.play(LaggedStartMap(
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ApplyMethod, dot_group2,
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lambda m : (m.scale_in_place, 0.5),
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rate_func = wiggle,
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lag_ratio = 0.05,
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run_time = 3,
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))
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self.wait()
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self.play(ReplacementTransform(rect1, rect3))
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for x in range(2):
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self.play(LaggedStartMap(
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ApplyMethod, dot_group3,
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lambda m : (m.scale_in_place, 0.5),
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rate_func = wiggle,
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lag_ratio = 0.05,
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run_time = 3,
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))
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self.wait()
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###
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def color_graph(self, graph, color1 = BLUE, color2 = WHITE, n_starts = 20):
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graph.set_color(color2)
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VGroup(*graph.dots[:11] + graph.lines[:10]).set_color(color1)
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def get_smoothed_velocity_graph(self, velocities):
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n = self.moving_average_n
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smoothed_vs = np.array([
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np.mean(velocities[max(0, i-n):i])
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for i in range(len(velocities))
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])
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return self.get_velocity_graph(smoothed_vs)
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def get_velocity_graph(self, velocities):
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n = len(velocities)
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dots = VGroup(self.get_dot(1, velocities[0]))
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lines = VGroup()
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for x in range(1, n):
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dots.add(self.get_dot(x+1, velocities[x]))
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lines.add(Line(
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dots[-2].get_center(),
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dots[-1].get_center(),
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))
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graph = VGroup(dots, lines)
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graph.dots = dots
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graph.lines = lines
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return graph
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def get_dot(self, x, y):
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dot = Dot(radius = 0.05)
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dot.move_to(self.coords_to_point(
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x * float(self.x_max) / self.n_data_points, y
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))
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return dot
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class ShowAllSteadyStateVelocities(SimpleVelocityGraph):
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CONFIG = {
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"x_axis_label" : "\\text{Domino spacing}",
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"x_min" : 0,
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"x_max" : 40,
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"x_axis_width" : 9,
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"x_tick_frequency" : 5,
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"x_labeled_nums" : list(range(0, 50, 10)),
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"y_min" : 0,
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"y_max" : 400,
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"y_labeled_nums" : [],
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# "y_labeled_nums" : range(200, 1400, 200),
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}
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def construct(self):
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self.setup_axes()
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for index in range(1, 20):
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index_str = ("%.2f"%float(0.01*index))[-2:]
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data_file = "data%s.txt"%index_str
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self.init_data(data_file)
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color = WHITE if self.friction == "low" else BLUE
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label = TextMobject(
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index_str,
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color = color
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)
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label.scale(0.5)
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label.set_color(color)
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dot = Dot(color = color)
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dot.scale(0.5)
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dot.move_to(self.coords_to_point(
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self.domino_spacing, self.velocities[-1] - 400
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))
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label.next_to(
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dot,
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random.choice([LEFT, RIGHT]),
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SMALL_BUFF
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)
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self.add(dot)
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self.add(label)
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print(index_str, self.velocities[-1], self.friction)
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class Test(Scene):
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def construct(self):
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shift_val = 1.5
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domino1 = Rectangle(
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width = 0.5, height = 3,
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stroke_width = 0,
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fill_color = GREEN,
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fill_opacity = 1
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)
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domino1.shift(LEFT)
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domino2 = domino1.copy()
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domino2.set_fill(BLUE_E)
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domino2.shift(shift_val*RIGHT)
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spacing = shift_val - domino2.get_width()
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dominos = VGroup(domino1, domino2)
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for domino in dominos:
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line = DashedLine(domino.get_left(), domino.get_right())
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dot = Dot(domino.get_center())
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domino.add(line, dot)
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arc1 = Arc(
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radius = domino1.get_height(),
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start_angle = np.pi/2,
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angle = -np.arcsin(spacing / domino1.get_height())
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)
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arc1.shift(domino1.get_corner(DOWN+RIGHT))
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arc2 = Arc(
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radius = domino1.get_height()/2,
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start_angle = np.pi/2,
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angle = -np.arcsin(2*spacing/domino1.get_height())
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)
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arc2.shift(domino1.get_right())
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arc2.set_color(BLUE)
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arcs = VGroup(arc1, arc2)
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for arc, vect in zip(arcs, [DOWN+RIGHT, RIGHT]):
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arc_copy = arc.copy()
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point = domino1.get_critical_point(vect)
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arc_copy.add_line_to([point])
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arc_copy.set_stroke(width = 0)
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arc_copy.set_fill(
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arc.get_stroke_color(),
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0.2,
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)
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self.add(arc_copy)
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domino1_ghost = domino1.copy()
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domino1_ghost.fade(0.8)
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self.add(domino1_ghost, dominos, arcs)
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self.play(Rotate(
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domino1,
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angle = arc1.angle,
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about_point = domino1.get_corner(DOWN+RIGHT),
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rate_func = there_and_back,
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run_time = 3,
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))
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self.play(Rotate(
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domino1,
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angle = arc2.angle,
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about_point = domino1.get_right(),
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rate_func = there_and_back,
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run_time = 3,
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))
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print(arc1.angle, arc2.angle)
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